Geodesic
An Inclusion Relation for Abel, Borel, and Lambert Summability
Canadian journal of mathematics, Tome 32 (1980) no. 3, pp. 695-702

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper a new type of inclusion theorem concerning Abel, Borel and Lambert summability is established. To state our results we need some definitions and notations. With a formal series ∑k=0 ∞a k , a k ∈ C, and its partial sums sn we associate the series Then ∑k=0 ∞ ak is said to be summable to the value s(a) by Abel's method, if (1.1) is convergent for |v| > 1 and limv→1+A(v)= s,(b) by Lambert's method, if (1.2) is convergent for |v| > 1 and limv→1+L(v)= s,(c) by Borel's method, if (1.3) is convergent for all x ∈ R and limx→+∞B(x)= s, 
Gawronski, W.; Siebert, H.; Trautner, R. An Inclusion Relation for Abel, Borel, and Lambert Summability. Canadian journal of mathematics, Tome 32 (1980) no. 3, pp. 695-702. doi: 10.4153/CJM-1980-054-5
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